Proposition 1.3 (Propositions 3-7, [1]}) 
Let \(B\)  be a left cancellative left semi-brace. Then, the map \(\lambda _a\)  given by \(\lambda _a(b):=a\circ (a^-+b)\)  is an automorphism of \((B,+)\)  and give rise to a homomorphism \(\lambda \)  from \((B,\circ )\)  to \(Aut(B,+)\)  by \(\lambda (a):=\lambda _a\)  for all \(a\in B\) . Moreover, the following properties hold:
